README.MD

Section 14

Parity, ECC, RAID

./section-14.pdf

1. Hamming ECC

1.1 How many bits do we need to add to 0011 to allow single error correction?

3

floor(log2(n_bits)) + 1

1.2 Which locations in 0011 would parity bits be included?

p1 p2 0 p4 0 1 1
1  2  3 4  5 6 7

1.3 Which bits does each parity bit cover in 0011?

1 2 3 4 5 6 7
p p 0 p 0 1 1

p1 - 1, 3, 5, 7
   -    0, 0, 1

p2 - 2, 3, 6, 7
   -    0, 1, 1

p4 - 4, 5, 6, 7
   -    0, 1, 1

1.4 Write the completed coded representation for 0011 to enable single error correction.

1 2 3 4 5 6 7
p p d p d d d
1 2 1 4 2 3 4

1 0 0 0 0 1 1
	      2

1.5 How can we enable an additional double error detection on top of this?

add additional parity bit over the whole seq.

1.6 Find the original bits given the following SEC Hamming Code: 0110111

1 2 3 4 5 6 7
0 1 1 0 1 1 1
p p d p d d d
1 2 1 4 2 3 4

p1 - bit = 0; seq = 1; error

p2 - bit = 1; seq = 1; match

p4 - bit = 0; seq = 1; error

1 + 4 = 5;

flip 5th to fix error
1 2 3 4 5 6 7
0 1 1 0 0 1 1	=>

1 0 1 1
	2

1.7 Find the original bits given the following SEC Hamming Code: 1001000

1 2 3 4 5 6 7
1 0 0 1 0 0 0
p p d p d d d
1 2 1 4 2 3 4

p1 - bit = 1; seq = 0; error

p2 - bit = 0; seq = 0; match

p4 - bit = 1; seq = 0; error

1 + 4 = 5;

flip 5th to fix error
1 2 3 4 5 6 7
1 0 0 1 1 0 0	=>

0 1 0 0
	2

2. RAID

		Configuration 			Pro 				Con

RAID 0		striping of data		simple storage			no redundancy
		across disks			management

RAID 1		traditional mirroring		easy cope with failures		amount of disks
		every data write also		by going to the mirror		expensive
		goes to backup disk
RAID 4
		independent read/write,		small reads			blocking write
		error detection within

RAID 5
		parity spread across the disks	multiple writes simultaneously
						as long as parity bits not
						located at the same disks